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integral of 2sin(5x)

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∫ 2sin(5x)dx

Solution

−25 cos(5x)+C

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∫ 2sin(5x)dx

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=2· ∫ sin(5x)dx

Apply u-substitution: ∫ sin(u)15 du

=2· ∫ sin(u)15 du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=2· 15 · ∫ sin(u)du

Use the common integral: ∫ sin(u)du=−cos(u)

=2· 15 (−cos(u))

Substitute back u=5x

=2· 15 (−cos(5x))

Simplify 2· 15 (−cos(5x)): −25 cos(5x)

=−25 cos(5x)

Add a constant to the solution

=−25 cos(5x)+C

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integral of 2sin(5x)

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